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comment by am_Unition
am_Unition  ·  2953 days ago  ·  link  ·    ·  parent  ·  post: Help me learn new things! – Chaos Theory

Check out bifurcation theory and diagrams. Here's a diagram I made yesterday showing x_n+1 = a*sin(pi*x_n), with alpha ("a") on the x-axis and x_n on the y-axis.

The system becomes truly chaotic around a=0.89.





ThurberMingus  ·  2953 days ago  ·  link  ·  

What do the different colors lines mean? I'm only vaguely familiar with bifurcation diagrams.

Devac  ·  2953 days ago  ·  link  ·  

Most likely different values of a / alpha although I can barely see the colours there so it could also be related to plot density. By the way, you can play with it on your own with Maxima and going through Chaotic dynamics with Maxima article.